Front propagation in Fisher–KPP equations with fractional diffusion.We study in this Note the Fisher–KPP equation where
the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the
fractional Laplacian. Contrary to what happens in the standard Laplacian case, where the stable state invades the unstable one
at constant speed, we prove here that invasion holds at an exponential in time velocity. These results provide a mathematically
rigorous justification of numerous heuristics about this model.